title: Boundary integral formulation for the electrical response of a nerve to an extracellular stimulation.
abstract: We present a two-dimensional boundary integral formulation of nerve impulse propagation. A nerve impulse is a potential difference across the cellular membrane that propagates along the nerve fiber. The traveling transmembrane potential is produced by the transfer of ionic species between the intra- and extra-cellular mediums. This current flux across the membrane-composed of conduction, diffusion and capacitive terms- is regulated by passive and active mechanisms that are highly complicated to describe mathematically from a microscopic point of view. Based on the Hodgkin and Huxley axon model, we propose a well-posed integral formulation based on a quasi-static approximation amenable to time-stepping schemes and discuss first results.
authors.forename: Fernando
authors.initials: F
authors.lastname: Henriquez
authors.forename: Carlos
authors.initials: C
authors.lastname: Jerez-Hanckes
authors.forename: M D Fernando R
authors.initials: MD
authors.lastname: Altermatt
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D004553:Electric Conductivity; D004558:Electric Stimulation; D005110:Extracellular Space; D006801:Humans; D009417:Nerve Tissue / Q000502:physiology*; D017711:Nonlinear Dynamics